VALUATION OF GENERAL CONTINGENT CLAIMS WITH SHORT SELLING BANS: AN EQUAL-RISK PRICING APPROACH

Abstract

This paper studies the valuation of general contingent claims with short selling bans under the equal-risk pricing (ERP) framework proposed in I. Guo & S.-P. Zhu (2017) [Journal of Economic Dynamics and Control 76, 136–151]. In existing literature, analytical pricing formulae were derived in the special case, where the payoff function is monotonic under risk-neutral measures. In this paper, we establish a unified framework for this new pricing approach so that its range of application can be significantly expanded. The results of I. Guo & S.-P. Zhu (2017) [Journal of Economic Dynamics and Control 76, 136–151] are extended to the case of non-monotonic payoffs (such as a butterfly spread option) under risk-neutral measures. We also provide numerical schemes for computing equal-risk prices under other measures such as the original physical measure. Furthermore, we demonstrate how short selling bans can affect the valuation of contingent claims by comparing equal-risk prices with Black–Scholes prices.